Congruum g : 900 <= g <= 999

Definition 1.

k²g=mn(m²-n²)
k, m, n, g in N (integer > 0)

Definition 2.

(x/z², y/z³) on elliptic curve Y²=X³-g²X
x, y, z in Z (integer)
X, Y in Q (rational)

X=mg/n, Y=kg²/n²

Type means,

1. m=i², n=j²
2. m=i², n=i²-j²
3. m=i²+j², n=i²
4. m=j², n=i²-j²
5. m=i²-j², n=j²

There are 35 congruum g : 900 <= g <= 999.
The solution of the following numbers are found.

902, 942

The solution of the following numbers are not in the range of 1 <= i, j <= 32,767.

911, 917, 919, 926, 933, 941, 958, 965,
967, 974, 982, 983, 989, 991, 997, 998

Congruum g : 900 <= g <= 999

g	m	n	x	y	z	type	i	j
901	3721	2025	3352621	5150065544	45	(1)	61	45
902	5281250	5276209	4763687500	14362042909500	2297	(3)	2297	71
903	875745649	61042800	875745649	25852906480393	260	(2) (4)	29593 30607	28543 29593
905	361	1	326705	186737700	1	(1)	19	1
	4173849	1739761	3777333345	211025876546700	1319	(1)	2043	1319
910	121	9	110110	36436400	3	(1)	11	3
	54184321	15855840	54184321	381391657919	132	(4)	8369	7361
	70040161	38328481	63736546510	13467813604845600	6191	(1)	8369	6191
915	121	1	110715	36837900	1	(1)	11	1
	7689529	368449	7035919035	589497714456300	607	(1)	2773	607
	53597041	1771440	53597041	392169563639	44	(4)	7441	7321
	61105489	5856000	61105489	475463076263	80	(2)	7817	7433
934	37827	37249	35330418	36570908232	193	(5)	274	193
935	2704	2209	2528240	2318444700	47	(1)	52	47
942	1673306	1190281	1576254252	43984943051580	1091	(3)	1091	695
943	43681	25281	41191183	215589527560	159	(1)	209	159
949	949	900	900601	271080901	30	(3) (5)	30 43	7 30
951	196	121	186396	63308070	11	(1)	14	11
957	734449	382800	734449	537168457	20	(2) (4)	857 1057	593 857
959	5184	4225	4971456	6423052104	65	(1) (5) (4)	72 97 97	65 65 72
966	25	21	1150	21160	1	(2)	5	2
	284089	96600	284089	142396813	10	(2) (4)	533 617	433 533
	380689	187489	367745574	6137572306320	433	(1)	617	433
973	5476	1251	38332	7306390	3	(2)	74	65
985	26569	6724	26170465	129522126825	82	(1)	163	82
	166465	166464	163968025	7277657725	408	(3) (5)	408 577	1 408
	737881	438244	726812785	15764201246625	662	(1)	859	662
987	336	289	331632	97416900	17	(5)	25	17
	484	141	3388	188650	1	(4)	25	22
995	320	121	318400	166324200	11	(5)	21	11
	40401	38809	40198995	70842228900	197	(1)	201	197
	2748964	1507005	547043836	10700818509466	549	(4)	2063	1658
	59320804	13662045	11804839996	1248117828653494	1653	(4)	8543	7702

• 1 <= ‚‡ <= 99
• 100 <= ‚‡ <= 199
• 200 <= ‚‡ <= 299
• 300 <= ‚‡ <= 399
• 400 <= ‚‡ <= 499
• 500 <= ‚‡ <= 599
• 600 <= ‚‡ <= 699
• 700 <= ‚‡ <= 799
• 800 <= ‚‡ <= 899
• 900 <= ‚‡ <= 999